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The **kinetic energy formula**, represented as KE = ½ × m v^{2}, establishes a relationship between the kinetic energy (KE) of an object, its mass (m), and the square of its velocity (v). By utilizing this formula, one can calculate the amount of kinetic energy possessed by an object based on its mass and the square of its velocity.

## Practice problems

### Problem #1

Calculate the kinetic energy of a ball with a mass of 3 kg and a velocity of 6 m/s.

**Solution**

Given data:

- Kinetic energy of a ball, KE = ?
- Mass of a ball, m = 3 kg
- Velocity of a ball, v = 6 m/s

Applying the formula:

- KE = ½ × m v
^{2} - KE = ½ × 3 × (6)
^{2} - KE = ½ × 3 × 36
- KE = 54 J

Therefore, the kinetic energy of a ball is **54 J**.

### Problem #2

What is the kinetic energy of a 6 kg bicycle moving with a velocity of 12 m/s?

**Solution**

Given data:

- Kinetic energy of a bicycle, KE = ?
- Mass of a bicycle, m = 6 kg
- Velocity of a bicycle, v = 12 m/s

Applying the formula:

- KE = ½ × m v
^{2} - KE = ½ × 6 × (12)
^{2} - KE = 3 × 144
- KE = 432 J

Therefore, the kinetic energy of a bicycle is **432 J**.

### Problem #3

Calculate the kinetic energy of an 800 kg car traveling at a velocity of 3 m/s.

**Solution**

Given data:

- Kinetic energy of a car, KE = ?
- Mass of a car, m = 800 kg
- Velocity of a car, v = 3 m/s

Applying the formula:

- KE = ½ × m v
^{2} - KE = ½ × 800 × (3)
^{2} - KE = 400 × 9
- KE = 3600 J

Therefore, the kinetic energy of a car is **3600 J**.

### Problem #4

A rail wagon weighing 400 kg has a velocity of 7 m/s. What is the kinetic energy of the rail wagon?

**Solution**

Given data:

- Mass of a rail wagon, m = 400 kg
- Velocity of a rail wagon, v = 7 m/s
- Kinetic energy of a rail wagon, KE = ?

Applying the formula:

- KE = ½ × m v
^{2} - KE = ½ × 400 × (7)
^{2} - KE = 200 × 49
- KE = 9800 J

Therefore, the kinetic energy of a rail wagon is **9800 J**.

## Related

## More topics

- Thermal energy equation
- Potential energy formula
- Gravitational potential energy formula
- Electric potential energy formula
- Elastic potential energy formula
**Kinetic energy formula**- Rotational kinetic energy formula
- Electrical energy equation
- Mechanical energy formula
- Photon energy equation
- Conservation of energy formula

## External links

- https://www.calculatorsoup.com/calculators/physics/kinetic.php
- https://www.omnicalculator.com/physics/kinetic-energy
- https://www.wikihow.com/Calculate-Kinetic-Energy
- https://www.khanacademy.org/science/hs-physics/x215e29cb31244fa1:modeling-energy/x215e29cb31244fa1:calculating-energy/v/calculating-kinetic-energy
- https://www.physicsclassroom.com/class/energy/u5l1c.cfm

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.